You state a lot of issue, lets see if we can get through a few:
Judgment - if you lived in the house you are responsible for the rent, even if there was no lease. They likely could have gotten a judgment against you, and still can if no agreement is reached.
New Lease - only you can decide if you want to sign. If you do not sign, you should be prepared to move out. The landlord will also likely continue the court case, and likely win. These sorts of cases are usually straight forward, unless there is some sort of notice problem. In this case it seems everyone is well notified. There may be some technical issues, however, that are not in the facts presented.
Things needing fixed - this should probably be part of your negotiations. Depending upon the severity of the problems, you may have the right to vacate the premises or pay for repairs and deduct from the rent. CHECK LOCAL REGULATIONS!!
Floor insulation - the easiest way to get this answer is to call a local contractor and ask what the codes require. Do this before signing a new lease, and add the issue to the negotiations.
The bottom line is that you are vulnerable to a judgment. Signing a new lease with a stipulation of paying back the late rent is a viable way to prevent the judgment.Ask a similar question